代数K理论在代数拓扑、数论、代数几何和算子理论等现代数学各个领域中的作用越来越大。这门学科的广泛性往往使人感觉望而生畏。本书以1990年秋天Maryland大学讲义为基础，不仅为数学领域研究生提供很好的学习代数K理论的基本知识，也讲述其在各个领域的应用。全书结构完整，了解代数基础知识、基本代数拓扑和几何拓扑知识就可以完全读懂这本书。该书也涉及到不少代数拓扑、拓扑代数和代数数论的知识。最后一章简明地介绍了循环同调以及其与K理论的关系。

Preface

Chapter 1.Ko of Rings

　1.Defining K0

　2.Ko from idempotents

　3.Ko of PIDs and local rings

　4.Ko of Dedekind domains

　5.Relative Ko and excision

　6.An application: Swan's Theorem and topological K- theory

　7.Another application: Euler characteristics and the Wall finiteness obstruction

Chapter 2.K1 of Rings

　1.Defining K1

　2.K1 of division rings and local rings

　3.K1 of PIDs and Dedekind domains

　4.Whitehead groups and Whitehead torsion

　5.Relative K1 and the exact sequence

Chapter 3.Ko and K1 of Categories, Negative K-Theory

　1.Ko and K1 of categories, Go and G1 of rings

　2.The Grothendieck and Bass-Heller-Swan Theorems

　3.Negative K-theory

Chapter 4.Milnor's K2

 1.Universal central extensions and H2

Universal central extensions

　 Homology of groups

　2.The Steinberg group

　3.Milnor's K2

　4.Applications of K2

　 Computing certain relative K1 groups

　 K2 of fields and number theory

　 Almost commuting operators

　 Pseudo-isotopy

Chapter 5.The +-Construction and Quillen K-Theory

　1.An introduction to classifying spaces

　2.Quillen's +-construction and its basic properties

　3.A survey of higher K-theory

　 Products

　 K-theory of fields and of rings of integers

　 The Q-construction and results proved with it

　 Applications

Chapter 6.Cyclic homology and its relation to K-Theory

　1.Basics of cyclic homology

　　Hochschild homology

　　Cyclic homology

　　Connections with "non-commutative de Rhom theory"

　2.The Chern character

　　The classical Chern character

　　The Chern character on Ko

　　The Chern character on higher K-theory

　3.Some applications

　　Non-vanishing of class groups and Whitehead groups

　　Idempotents in C*-algebras

　　Group rings and assembly maps

References

　　Books and Monographs on Related Areas of Algebra,Analysis, Number Theory, and Topology

　　Books and Monographs on Algebraic K-Theory

　 Specialized References

Notational Index

Subject Index